Dam construction.



L. JORGENSEN. DAM CONSTRUCTION. APPLIGATION FILED 001214, 1910.

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DAM CONSTRUCTION. ABPLIOATION FILED 00114, 1910.-

986,71 8; Patented Mar. 14, 1911.

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wi/fmeooeo a I I L. JORGENSEN. DAM GONSTRUGTION.

APPLICATION FILED QOT. 14, 1910.

L. JORGENSEN.

DAM CONSTRUCTION. APPLIUATION-IILED 00T.14, 1910.

Patented Mar. 14, 11911.

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33 affoznez s' UNITED STATES- PATENT OFFICE.

LABS aonennsnn, or

BERKELEY, CALIFORNIA, ASSIGNOR OF ONE-HALF T FRANK G. BAUM, OF SAN FRANCISCO, CALIFORNIA.

' DAM cons'rnuo'rron.

Patented Mar. 14,1911.

To all whom it may cancer-1i: Be it known that I, LABS JoRoENsnN, a citizen of the United States, residing at Berkeley, in the county of Alameda and State of California, have invented certain new and useful Improvementsin DamConstruction, of which the following is a full, clear, and exact'description.

. This invention relates to dam constructions, and has for its object the development of a dam body, the volume of which is reduced to a minimum while afl'ording a maximum of efliciency and strength. My improved dam construction therefore results' waterpressure. This isavery uneconomical way of using the material, such for example as concrete, of whichthe dam is to be constructed, as such material at the toe. of the dam is very highly compressed, while ,other parts have little or no compression at all. In so far as I am aware, arch dams as heretofore constructed have used an arch of sub.- stantially but a single radius; that is, the radius of the arch at the bottom where the valley or cafionis narrow, has-been the same,

or substantially the same,-as theradius of the arch at the top; the only increase in' radius which has at all been provided: for being due to the, slope of the faceof the dam; all ofthe radii being struck from a common center or axis.

As above indicated the principal objects of my invention have been to economize material and, correlatively, labor; practically every portion of material inthe dam body being disposed to the best possible advantage.

Other objects of my invention will be hereinafter set forth and more particularly pointed out in the appended claims.

Referring to the accompanying drawings,

which form a part hereof: Figure 1 is a plan Application filed October 14, 1910. Serial No. 586,969.

view of a dam constructed in accordance with'the principles of my invention; topographical or contour lines of a canon in which the said dam is positioned being indicated. Fig. 2 is a plan view of an arch dam; illustrating the usual assumption that any curved dam is a-portion of a cylinder ring; this figure being used as a basis for the computation hereinafter referred to. Fig. 3

shows a curve utilized in determining values usedin said computation. Fig. 4 is a vertical transverse section taken on the line AB of Fig. 1. Fig. 5 is a similar section taken on the line C-D of said figure; Fig. 6 is an enlarged fragmentary section corresponding to that portion of the section shown in Fig.

v4: which lies between levels II III; but :showmg the substitution of hollow-cylinder. sectors for the frustum of a cone or approximate cone indicated in Fig. 4:, at such portionof the section. Fig. 7 is a comparative study of several forms of dam sections; showln the material decrease in volume effected y constructing the dam in accordance with the principles of the invention herein described.

Referring to said drawings, in hich like reference characters designate 11 parts throughout the several views; and starting with the assumption which is usually made that any curved dam,'such as that for example shown at 1, in Fig. 2,'is'a portion of a cylinder ring 2, in which the average stress I 9, expressed in pounds per square foot, is equal to the radial load P (in pounds per square foot), multiplied by the radius of the exterior face and divided'by the area of the section; as per equation P R-l-t V being the volume, R -the mean radius 249 the inclosed angle indicated in Fig. 2, and

0, the constant. The mean radiusR equals the inner radius plus half the thickand in. 2 the relative values of this term are graphically. shown by the curve 3,

25 constitute the abseiss'ae'and the values of 35 steep walls, will be a minimum when the '60 to; cover practical cases of this character'I andialso' equals half the width W,of

the canon divided by the sin. of half the incldsed angle:

' 'R'm =R+ q sinfi Now-gs the arjea of the darn] section varies with the mean radius; the volume of 0 masomyiws'inffi I in which" C and K are constants, the latter de'ending uponthe width of. the canon;

rom nation tit is seen that the volume. varies wit ,7 l

I "in 'which the various angles representing sinffl I constitute the ordinates; the latter for rea sons above set forth corresponding to the percentages of volume of masonry, From this curve it will be seen that the amount of masonryrequired for any curved or arched dam, at' least in .a canon with relatively mean radius is so chosen'that the inclosed angle 20is about 133; and the curve also 5' -shows.that-the variation in the amount of masonry required for a given dam will only 40 be.;about one per cent. provided that the I vvalues of 20 beheld between the limits of 3120and 146. Outside of these limits the increase'in amount of masonry required is 've rapid; and hence the length'of the described hereinafter will, as far as ossible, .be scchosen that 20 can be" kept 'etween these limits.

The dam' must of course be safe when 'the' must, in some cases,'be prevented by increas- 1 ingthe thickness above thatfound from the formula,.in which 'case it is most economical to throw-normal-load on the total'area by in-' for .the'reason that. a relatively flat arch; requires less, material than a" more-curved one. By flattening the arch the inclos'ed. angle. is necessarily'decreas'ed andin. order 7 desire. to state that I. considerthe varying'of tl.e inclosed angles 20 of the dam sectors between thelimits and 140 to be within the purview of m invention.

"sfi'dered primaril asfan independent strucrtui'e; such'slices ing thereafter superposed determining the contour of the walls of the limit (146) for great economy, and at the disclosed involves the independent determination of the dimensions of successive arch shaped slices of the dam lying between predetermined levels; each slice'beingconor substantially superposed to form 'the dam .body.

Referring nowto Fig. 1, the procedure of dam therein shown is substantially as follows: A topographical survey of the canon or valley should. first bemade and the contour lines should be lotted as indicated in the said figure. 'In t e present instance six elevations'or levels have been established forming respectively the contour lines I, II,

III, 1111, V and VI, the contour lines VI corresponding tola level which will'be substantiallythat of the level of the water retained by the dam when the latter is completed, while the contour lines I I correspond to substantially the lowest d am level in the orge orvalley; the remain n lines being those of intermediate levels. .T e distan'ceiacross the canon W, at thetop con-.

tour VI of the dam is ascertained. Then the mean" radius, v

which will give the dam the greatest strength with the least volume'of material is found .bymeans of Fig. 2. 'At this parmean radius will bei it i 's1n.0- 0 bei n selected by means of Fig. 2. 'At the top 0 the dam it will be generally found of advantage to choose 20 near the upper bottom to correspondingly choose 20 near the lower limit After the most economical mean radius for this elevation has been ascertained, the thickness't may be algebraically determined, from the fore- 115 going equations. The first relatively abrupt: change of 'sl'opeof; the cafion sides preferablycoincides with elevation or level V;

the distanceacross-the canon 'atthis elevation being measured and the most economicalmean radius of the section at suchlelevation is found by meanslof the curve shown injFig. 2,]in the same way asthe. corres ondmg mean adius was determined for e ovation fter the radius has been settled upon, the thickness t; iscomputed and the'up-stream' radius" (RH-t -is correspondingly also determined. The center of curvature of the arch slice at elevation V 65 The method 0 dam construction, herein l with a thickness t, doesfnot necessarily lie ,130

:ticular'elevation (VI) the most economical 7 seems on the same center line as the center of curvature of the arch slice at elevation VI; in fact it practically never will do so, as perfectly even slopes of the respective canon sides or walls will rarely be found. Hence the shape of'the surface of the up-stre'a-m face of the dam between elevations VI and V cannot be described as resembling that of any known geometrical body. In general it may be said to have ,a surface resembling that of-a sector offthe'fi'ustum of a cone. Elevation 1111 is coincident with another change of slope in the sides of the cation;

and themost economical mean radius correspondlng to the fixed distance W across the cafion at this level is found in the same manner as were-found the corresponding mean radii for elevations'VI and V; andthe location of the center of curvatureof the arch slice at this elevation is again chosen regardless of the location of the centers of the slices at elevations VI and V. III-other words, the dam has no common center line,

and centers are located principally with a.

view to getting the length of the arch as short as possible for a givenidistance across the canon, and in View of the deducted most economical mean radius for such given dis-' tance. Theradii and thicknesses at elevations III, II and I are correspondinglydetermined in accordance with the procedure above outlined. After having calculated the different radii and respective'thicknesses of the several sectors of the dam, the top thickness is set ofi and the arcs of two concentric cir-.

. cles with radii R and (R -H respectivelyd the are drawn in on the contour map; an

centers of suchcircles will ibe, of course, 011

a line drawn, perpendicular to the center of the chord W The thickness t, is then set ofi and the arcs of two other concentric circles, respectively .with radii R and (R -H are drawn in until intersection occurs with the contour line V- V; bearing in mind that the 'centercommon to these latter two circles does not need to be the perpendicular to the chord W above reerred to. These circles, concentric only in pairs, determine the contour of the dam between elevations VI and V, It is usually.

convenient and preferable to asswne 4 the down stream faces of the upper slices of the dam adjacent the center thereof, to be vertical, at least for thefirsttrial; although after the lower slices have been laid in, it may at times, be found desirable to slope the-central portion of such face one way or thet'other'." The center of the arch slice at elevation V'V is correspondingly disposed on a perpendicular drawn through the center of the chord W and the thickness 2? is set off, assuming initially again that the central portion of the down stream face is v substantially vertical here also; although j fsome slope may thereafter be given to it. It

'hasbeen found in practice that a vertical wall at this point usually afi'ords the most economical construction. At' other vpoints the down stream face will ordinarily have some slope, due to the above method of 'construction. The arcs of twoconcentric circles with radii R and (Rd-t respectively are then drawn in until intersection occurs with contour lines IVIV bearing in mind again that'the center common to these two circles does not need to and hardly ever will lie on.,

spective sectors, especially where a very abrupt change occurs only at one side or upon one wall of the cafio'n. In general, too, lt-is 'desirable, where possible, to bring the sets of arcs of concentric circles which are disposed in thepex't succeeding elevation as nearly beneath those in the adjoining elevation as possible, so that the respective sectors of the .dam may be as nearly superposed .as the contour of their-faces Will permit; Of .conrseit willbe impossible owing to, the differences .in'contour of'the respective sections :to secure .exact coincidence, v

and, hence the respective: complete lateral faces of the dam both uponthe stream side and upon the concave side thereof will be of rather irregular contour, each of said surf-aces somewhat resembling a warped sur face. 'In practice, as will be seen from an inspection of Fig. 1, portions of contiguous horizontally alined points in one or the other faces of the dam. will n rmally project out laterally in varying degrees beyond other horizontally alined points which are disposed substantially in parallelism with those first mentioned. For example,

considering the convex or stream side of the dam, it will be seen'that'the 'substantially vertical surface of one'of the lower v sectors will project out laterally i n .vary1ng'.

degrees beyond the correspondingpoints in one'of the upper sectors; on in other words,

thedist-ance a-indicated in liig. -1 .will be different from the distance 6 in ,the same figure, although such distances are measured in the same horizontal plane.

While it is generally preferable to so form the respective slices or, sectors of the dam, which lie. between the severaleleva- ,tions of such configuration, that the respective tops and bottoms ofadjoining slices may be regarded as being superposed n strlct coincidence in the manner shown. in;

Figs. 4- and 5, itis desirable in some lo-- calities to face the dam with ashlar, cutstones, or the like, and itimay be of advantage in such case to stepthe faces of the dam however, are'ascertained in exactly the sa e manner as in the foregoing, and these ho low-cylinder sectors whenjviewed from the top each a-ppea'r substantially as an arch like that shown-in Fig. 2, while each step of the section shown in Fig. 6 corresponds to a sector and shows the height of the same; the height of each sector being uniform throughout the length thereof, and in this exeniplification of my invention the width T being of course also uniform throughout. It is also desirable for various practical considerations, to thicken some- Whatthe upper section, or at le'ast the upper portion thereof; so that the thickness of the dam at this point will be greater tl1l1'1 the calculated thickness, as shown at 4 in Fig. 7.

In conclusion I desire to call attention to the fact that while I have proposed substantially 133 as the best angle for use in the dam construction, in practice it is frequently desirable to choose a larger angle at the top, as for instance 140; since in many cases the use of a considerably smaller angle may be necessitated near the bottom.

What I claim,is:- F 1. An arch dam for a cafion or the like comprising a plurality of superposed arch shaped elements of varying radii the radii of such elements varying with the widths of the canon at the corresponding levels of such elements and bearing a definite relation to such Widths.

2. An arch dam comprising superposed arch shaped elements of varying radii, the centers of curvature of such elements being out of vertical. alinement.

3. An arch dam comprising superposed arch shaped elements of varying radii and thickness, the radii and thickness "of such elements varying with the widths of the canon at the correspondin levels of such elements and bearing a de nite relation to such widths-and to the pressure to which they aresubjected.

.4. An arch dam fora cafion or thelike comprising a monolith, a wall of which is of irregular contour and resemblesa warped surface;

5. An arch dam having a face thereof of irregular contour, resembling a warped surface, parts of the lower portion of said surface lying in the same horizontal plane projecting in varying degrees out beyond the upper portion thereofcorresponding,

parts in an upper portion of said surface, lying in a second horizontal plane.

6. An arch dam having the convex face thereof of irregular contour, thelowerporzontallyalined points disposed substantially i in' parallelism with, but vertically displaced with respect to, those first. mentioned.

8. An arch dam having the concave face thereof ofirregular. contour, the lower portions of said face projecting out beyond the corresponding upper portions and the lower portions adjacent the sides of the dam projecting farther than those adjacent the cen ter thereof.

9. An arch dam formed of a plurality of sectors the angles of which are between substantially 60 and 140, said sectors being of different radii of curvature, the axes of curvature of the respective sectors being non-coincident. v

10. A dam body for a cafion or'the like,

comprising a plurality of superposed hollow sectors of differing radii, the radius of .the middle element of the convex face of each of said sectors bearing a definite relation to the width of the cafion at the level difi'ering radi1,.the relative heights of said sectors being determined' by the vertical ,distances between levels taken through abrupt changesin the slope of the cafion sides.

12., A dam body formed of a plurality of hollow. sectors of differing radii, the axes of curvature of said sectors being non-coir cident, and the lateral thickness of each sector, along any 'ven horizontal level, being substantially uniform throughout the length of said sector.

In witness whereof, -'I subscribe my signature, in the presence of two witnesses.

. LABS .JORGENSEN. 

